Yes, they should, however they should of course also use their head and realize that sometimes it's better to not use it yet. That's rare though.

My Ops group runs 2 Op healers and 2 Sin tanks.

Over 50% of our in-combat rezzes are not battle rezzes.

It depends on group makeup obviously, and individual competence, but saying that anyone should automatically battle rezz is a little silly. It is always situational, and if there's any ambiguity whatsoever, the raid leader should make the final call (and live with the consequences).